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A Fano factor measurement for silicon using low energy photons
NUCLEAR
INSTRUMENTS
AND
METHODS
76 (I969) 59-6o;
© NORTH-HOLLAND
PUBLISHING
CO.
A FANO FACTOR MEASUREMENT FOR SILICON USING LOW ENERGY PHOTONS J. M. P A L M S , P. V E N U G O P A L A
R A O a n d R. E. W O O D
Department of Physics, Emory University, Atlanta, Georgia 30322, U.S.A. Received 10 J u n e 1969 T h e F a n o factor in silicon at liquid nitrogen t e m p e r a t u r e is m e a s u r e d to be F = 0.1434-0.006 u s i n g p h o t o n s f r o m 6.40 to 74.97 keV. N o energy dependence o f the value o f F is f o u n d in
t h e r a n g e o f t h e present m e a s u r e m e n t s . E x t r e m e care was t a k e n to eliminate possible errors caused by electronic pulse shaping, electronic gain stability a n d pile-up effects.
1. Introduction
to the broadening of the full energy peak such as (a) electronic gain stability, (b) pile-up effects at fast count rates, and (c) the "geometry effect"lg). These effects must be accounted for in any accurate measurement of F. Careful monitoring of experimental conditions can usually account for (a) and (b). The "geometry effect" is expected to have a small influence on the present measurements. Several techniques have been suggested to account for the line broadening due to the electronics and the
In the past several years a considerable number of measurements have been made of the Fano factor, F, for Ge x-6) and Si 7.12) using betas and gammas on surface barrier and lithium drifted detectors. However, only one value of F for Si has been measured with low energy photons with special effort to account for carrier trapping7). There is considerable difficulty in measuring F a n d therefore disagreement on accuracy of the measurements still exists. This can be appreciated by considering the contributions to the observed resolution in a semiconductor spectrometry system responding to monochromatic photons. The observed full width at half m a x i m u m (fwhm) of the full energy peak is (fwhm)2b = (fwhm)2+t+ (fwhm)+t¢ 2 ¢ + (fwhm)¢ot,, 2
(1)
where
(fwhm)d.,
is the detector contribution to the resolution considered to be the statistical spread in the production of electron-hole pairs. For a Gaussian distribution this is related to the Fano factor by the relation (fwhm)~ a = 2.352F~E, (2)
3 e ~ -~" ~ z
• •
• •
where
and E (fwhm)e~e~ (fwhm)~ou
is the energy necessary to create an electron-hole pair, which is 3.81 eV for Si at 77°K la) and 2.98eV for Ge at 77°KE,la), is the energy of the incident photon in eV. is the electronic noise contribution, and is the contribution due to incomplete charge collection in the detector.
74.97 68.88 L4.39 6.59
keV keV k¢~/ kW
[-o
~g :S :z
The accurate measurement of a value for the Fano factor is therefore only possible if the contributions to the line broadening due to electronic noise and incomplete charge collection are eliminated. In principle this is simple, but experimentally this is difficult to achieve. There are other factors which can contribute
II
i
L
t
i
2
3
4
5
(BIA
S)
i 6
-2
Fig. 1. (fwhm)o%- (fwhm)~2~¢ plotted against (detector bias) -2, where the bias is in kV.
59
60
j . M . PALMS et al.
charge collection inefficiency. One way is to measure the (fwhm)ob as a function of detector bias, A plot is made of (fwhm)ob, v-,~o against the photon energy E. The value of F is then deduced from the shape of a straight-line fit through these points. This method assumes that F and e are independent of energy. In another method Zulliger et al. 7) used a precision electronic pulser to find (fwhm)2~¢~. They also showed that (fwhm)2oll is proportional to (l/V) 2. They then plot [(fwhm)2b- (fwhm)21j ~ as a function of 1/V; a straight-line fit extrapolated to infinite field gives (fwhrn)det. This involves the assumption that the carrier velocities are proportional to the bias which is not strictly true for high fields. Our technique for arriving at (fwhm)dzet is somewhat similar to this technique, however, we think it better to plot (fwhm)o2b-(fwhm)21o¢ as a function of (l/V) 2, which should be a straight line. A straight-line fit extrapolated to infinite field gives an upper limit to (fwhm)], t. The Fano factor is then calculated from eq. (2). If F does not depend on E a straight-line fit to a plot of ( f w h m)) 2 ~ 2h eE m ) e. 2 ~ 3 versus 5 ( 1
precision pulser. Count rates less than 1000 counts per sec were used. A Gaussian peak fit was used on the full energy and pulser peaks with a calibration of approximately 20 eV per channel on the analyzer. The fwhm in eV deduced in this matter were measured as a function of detector bias in kV. 3. Results and conclusion The results of these measurements are shown in fig. 1, which shows (fwhm)2b-(fwhm)21e c plotted against (l/V) 2, Vin kV. The upper limit of F calculated from eq. (2), is found to be 0.143___0.006. The value was found to be independent of energy. The value of F = 0.143+__0.006 compares very favorably with the recent value of 0.15(+ 0.01, - 0.02) obtained by Zulliger et al.7). We feel that our value is an upper limit and could be somewhat lower. The value agrees well with the theoretically predicted value of 0.15 as made by Van Roosbroeck15), but not with recent other predictions by Klein 8) (F = 0.05) and Di Cola and Farese 16) (F = 0.28). References
will yield F as (1IV 2) --~ O. 2. Experiment The silicon detector used was a Kevex, Si(Li) photon spectrometer of 4 mm depletion depth having a resolution of 290 eV (fwhm) for the Fe K, X-rays (6.4 keV). The output of the cooled FET preamplifier was fed through a Tennelec Model TC-200 amplifier into T M C Model 1001 multichannel analyzer. The electronic resolution was measured simultaneously for each gamma-ray source with a Tennelec Model TC-800 TABLE 1 P h o t o n source used. Source 57Co 2°7Bi 204T1
Photon energy 6.40 14.39 74.97 68.89
keV (K~ o f Fe) keV keV (K~I o f Pb) keV (Kaz o f Hg)
1) G. T. Ewan and A. J. Tavendale, Can. J. Phys. 42 (1964)2286. 2) S. O . W . A n t m a n , D . A . Landis and R . H . Pehl, Nucl. Instr. and Meth. 40 (1966) 272. ~) H. M. Mann, H. R. Bilger and 1. S. Shermann, IEEE Trans. Nucl. Sci. NS-13, no. 3 (1966) 252. 4) R . L . Heath, W . W . Black and J . E . Cline, IEEE Trans. Nucl. Sci. NS-13, no. 3 (1966) 445. 5) H. R. Bilger, Phys. Rev. 163 (1967) 238. 6) j. M. Palms, P. Venugopala Rao and R . E . Wood, Nucl. Instr. and Meth. 64 (1968) 310. 7) H. R. Zulliger, L. M. Middleman and D. W. Aitken, IEEE Trans. Nucl. Sci. NS-16, no. 1 (1968) 47. 8) C. A. Klein, IEEE Trans. Nucl. Sci. NS-15, no. 3 (1968) 214. 9) G. Bertolini and A. Coche, Semiconductor detectors (Wiley, New York, 1968), lo) R. L. Heath, private communication. 11) O. Meyer and H. J. Langmann, Nucl. Instr. and Meth. 39 (1966) 119. 12) p. Siffert, A. Coche and F. Hibou, 1EEE Trans. Nucl. Sci. NS-13, no. 3 (1966) 225. 13) R. H. Pehl, F. S. Goulding, D. A. Landis and M. Lenzinger, Nucl. Instr. and Meth. 59 (1968) 45. 14) R . B . Day, G. Dearnaley and J . M . Palms, IEEE Trans. Nucl. Sci. NS-14, no. 1 (1967) 487, 15) W. Van Roosbroeck, Phys. Rev. 139 (1965) A 1702. 16) G. Di Cola and L. Farese, Phys. Rev. 162 (1967) 690.
INSTRUMENTS
AND
METHODS
76 (I969) 59-6o;
© NORTH-HOLLAND
PUBLISHING
CO.
A FANO FACTOR MEASUREMENT FOR SILICON USING LOW ENERGY PHOTONS J. M. P A L M S , P. V E N U G O P A L A
R A O a n d R. E. W O O D
Department of Physics, Emory University, Atlanta, Georgia 30322, U.S.A. Received 10 J u n e 1969 T h e F a n o factor in silicon at liquid nitrogen t e m p e r a t u r e is m e a s u r e d to be F = 0.1434-0.006 u s i n g p h o t o n s f r o m 6.40 to 74.97 keV. N o energy dependence o f the value o f F is f o u n d in
t h e r a n g e o f t h e present m e a s u r e m e n t s . E x t r e m e care was t a k e n to eliminate possible errors caused by electronic pulse shaping, electronic gain stability a n d pile-up effects.
1. Introduction
to the broadening of the full energy peak such as (a) electronic gain stability, (b) pile-up effects at fast count rates, and (c) the "geometry effect"lg). These effects must be accounted for in any accurate measurement of F. Careful monitoring of experimental conditions can usually account for (a) and (b). The "geometry effect" is expected to have a small influence on the present measurements. Several techniques have been suggested to account for the line broadening due to the electronics and the
In the past several years a considerable number of measurements have been made of the Fano factor, F, for Ge x-6) and Si 7.12) using betas and gammas on surface barrier and lithium drifted detectors. However, only one value of F for Si has been measured with low energy photons with special effort to account for carrier trapping7). There is considerable difficulty in measuring F a n d therefore disagreement on accuracy of the measurements still exists. This can be appreciated by considering the contributions to the observed resolution in a semiconductor spectrometry system responding to monochromatic photons. The observed full width at half m a x i m u m (fwhm) of the full energy peak is (fwhm)2b = (fwhm)2+t+ (fwhm)+t¢ 2 ¢ + (fwhm)¢ot,, 2
(1)
where
(fwhm)d.,
is the detector contribution to the resolution considered to be the statistical spread in the production of electron-hole pairs. For a Gaussian distribution this is related to the Fano factor by the relation (fwhm)~ a = 2.352F~E, (2)
3 e ~ -~" ~ z
• •
• •
where
and E (fwhm)e~e~ (fwhm)~ou
is the energy necessary to create an electron-hole pair, which is 3.81 eV for Si at 77°K la) and 2.98eV for Ge at 77°KE,la), is the energy of the incident photon in eV. is the electronic noise contribution, and is the contribution due to incomplete charge collection in the detector.
74.97 68.88 L4.39 6.59
keV keV k¢~/ kW
[-o
~g :S :z
The accurate measurement of a value for the Fano factor is therefore only possible if the contributions to the line broadening due to electronic noise and incomplete charge collection are eliminated. In principle this is simple, but experimentally this is difficult to achieve. There are other factors which can contribute
II
i
L
t
i
2
3
4
5
(BIA
S)
i 6
-2
Fig. 1. (fwhm)o%- (fwhm)~2~¢ plotted against (detector bias) -2, where the bias is in kV.
59
60
j . M . PALMS et al.
charge collection inefficiency. One way is to measure the (fwhm)ob as a function of detector bias, A plot is made of (fwhm)ob, v-,~o against the photon energy E. The value of F is then deduced from the shape of a straight-line fit through these points. This method assumes that F and e are independent of energy. In another method Zulliger et al. 7) used a precision electronic pulser to find (fwhm)2~¢~. They also showed that (fwhm)2oll is proportional to (l/V) 2. They then plot [(fwhm)2b- (fwhm)21j ~ as a function of 1/V; a straight-line fit extrapolated to infinite field gives (fwhrn)det. This involves the assumption that the carrier velocities are proportional to the bias which is not strictly true for high fields. Our technique for arriving at (fwhm)dzet is somewhat similar to this technique, however, we think it better to plot (fwhm)o2b-(fwhm)21o¢ as a function of (l/V) 2, which should be a straight line. A straight-line fit extrapolated to infinite field gives an upper limit to (fwhm)], t. The Fano factor is then calculated from eq. (2). If F does not depend on E a straight-line fit to a plot of ( f w h m)) 2 ~ 2h eE m ) e. 2 ~ 3 versus 5 ( 1
precision pulser. Count rates less than 1000 counts per sec were used. A Gaussian peak fit was used on the full energy and pulser peaks with a calibration of approximately 20 eV per channel on the analyzer. The fwhm in eV deduced in this matter were measured as a function of detector bias in kV. 3. Results and conclusion The results of these measurements are shown in fig. 1, which shows (fwhm)2b-(fwhm)21e c plotted against (l/V) 2, Vin kV. The upper limit of F calculated from eq. (2), is found to be 0.143___0.006. The value was found to be independent of energy. The value of F = 0.143+__0.006 compares very favorably with the recent value of 0.15(+ 0.01, - 0.02) obtained by Zulliger et al.7). We feel that our value is an upper limit and could be somewhat lower. The value agrees well with the theoretically predicted value of 0.15 as made by Van Roosbroeck15), but not with recent other predictions by Klein 8) (F = 0.05) and Di Cola and Farese 16) (F = 0.28). References
will yield F as (1IV 2) --~ O. 2. Experiment The silicon detector used was a Kevex, Si(Li) photon spectrometer of 4 mm depletion depth having a resolution of 290 eV (fwhm) for the Fe K, X-rays (6.4 keV). The output of the cooled FET preamplifier was fed through a Tennelec Model TC-200 amplifier into T M C Model 1001 multichannel analyzer. The electronic resolution was measured simultaneously for each gamma-ray source with a Tennelec Model TC-800 TABLE 1 P h o t o n source used. Source 57Co 2°7Bi 204T1
Photon energy 6.40 14.39 74.97 68.89
keV (K~ o f Fe) keV keV (K~I o f Pb) keV (Kaz o f Hg)
1) G. T. Ewan and A. J. Tavendale, Can. J. Phys. 42 (1964)2286. 2) S. O . W . A n t m a n , D . A . Landis and R . H . Pehl, Nucl. Instr. and Meth. 40 (1966) 272. ~) H. M. Mann, H. R. Bilger and 1. S. Shermann, IEEE Trans. Nucl. Sci. NS-13, no. 3 (1966) 252. 4) R . L . Heath, W . W . Black and J . E . Cline, IEEE Trans. Nucl. Sci. NS-13, no. 3 (1966) 445. 5) H. R. Bilger, Phys. Rev. 163 (1967) 238. 6) j. M. Palms, P. Venugopala Rao and R . E . Wood, Nucl. Instr. and Meth. 64 (1968) 310. 7) H. R. Zulliger, L. M. Middleman and D. W. Aitken, IEEE Trans. Nucl. Sci. NS-16, no. 1 (1968) 47. 8) C. A. Klein, IEEE Trans. Nucl. Sci. NS-15, no. 3 (1968) 214. 9) G. Bertolini and A. Coche, Semiconductor detectors (Wiley, New York, 1968), lo) R. L. Heath, private communication. 11) O. Meyer and H. J. Langmann, Nucl. Instr. and Meth. 39 (1966) 119. 12) p. Siffert, A. Coche and F. Hibou, 1EEE Trans. Nucl. Sci. NS-13, no. 3 (1966) 225. 13) R. H. Pehl, F. S. Goulding, D. A. Landis and M. Lenzinger, Nucl. Instr. and Meth. 59 (1968) 45. 14) R . B . Day, G. Dearnaley and J . M . Palms, IEEE Trans. Nucl. Sci. NS-14, no. 1 (1967) 487, 15) W. Van Roosbroeck, Phys. Rev. 139 (1965) A 1702. 16) G. Di Cola and L. Farese, Phys. Rev. 162 (1967) 690.